Trig identities problem! Pls help

Question

This is the given: csc (θ) = 5 and theta is in Quadrant 2,

What is cot(θ) - cot(π-θ) + cot(θ-2π)?

Answer 1

As csc(θ) = 5, sin(θ) = 1/csc(θ) = 1/5

As we are in Quadrant 2, cos(θ) = -√(1 - sin²(θ)) = -√(1 - (1/5)²) = -√24 / 5

Thus, cot(θ) = cos(θ)/sin(θ) = -√24 / 5/(1/5) = -√24 = -2√6

cot(θ - 2π) =cot(θ)

cot(π - θ) = -cot(θ)

Thus, cot(θ) - cot(π - θ) + cot(θ - 2π) = 3 cot(θ) =3(-2√6) = -6√6